Question

Represent √3 on number line

Answer 1

First draw a number line having points (at least) [0,3]. If we denote the point 0 as “O” and point 1 as “A” then OA will be equal to 1 unit. Then at point A draw a perpendicular of length AB=1 unit ( equal to the distance from 0 to 1 in the number line i.e. OA). And join the points O and A, so that OAB is a right angled triangle. Then by pythagoras theorem,

OB^2=OA^2+AB^2

=> OB=sqrt (1^2+1^2)

=>OB = root2

Now, again draw a perpendicular at point B of length BC= 1 unit and join the points O and C. Again by pythagoras theorem we get OC = root 3. Then by compus taking radius =OC, draw an arc so that it cuts the number line at D. Then the distance OD will be the square root of 3.

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Answer 2

Step-by-step explanation:

• Draw a number line and mark point O
• Mark point A on it such that OA = 1 unit
• Draw right triangle OAB such that ∠A = 90° and AB = 1unit
• Join OB
• By Pythagoras Theorem , OB =$\sqrt{ 1^2 +1^2} = \sqrt{ 2 }units$
• Draw a line BC perpendicular to OB such that BC = 1
• Join OC
• Thus OBC is a right angled triangle. Again by Pythagoras theorem , we have $OC = \sqrt{(\sqrt{2} )^2 +1^2} =\sqrt{3} units$
• With center as O and radius OC draw a circle which the number line at a point E
• $OE = \sqrt{3} units$ Thus OE represents $\sqrt{3}$ on the number line